Research On Distributed Optimization Flocking Of Nonlinear Multi-agent Systems

Graph theory and stability theory of Lyapunov are used to prove that the stability of the system and minimize the total cost function by using only local interaction and information,thus achieving optimization.The paper mainly completed the following three aspects:Firstly,the distributed optimization problem of multi-agent systems with flocking behavior is studied.Second order dynamical systems are considered.A distributed controller is composed of collision avoidance term,speed control term and optimization term.The control algorithm is deduced and the convergence and stability of the algorithm are proved by using the stability theory.Secondly,the adaptive distributed optimization of multi-agent systems with flocking behavior is studied.A good adaptive controller can readjust its characteristics under the changing environment,so that the system can run stably and enhance efficiency.Based on this,a distributed adaptive control rule is proposed,which makes the system achieve flocking and optimization.Thirdly,the distributed optimization of heterogeneous multi-agent systems is studied.Heterogeneous systems are composed of agents with two different types of dynamical behaviors.The consensus and optimization are proved by using the properties of Kronecker product and non-smooth analysis.Finally,the effectiveness of the method is verified.